An Analytic Solution to the Unsymmetrical Bending Problem of Diaphragm Coupling

As the rigidity of either the hub or rim of the diaphragm coupling is much larger than that of the disk,and the unsymmetrical bending is under the condition of high speed revolution,a hypothesis was supposed that each circle in the middle plane before deformation remains its radius unchangeable after deformation but the plane on which the circle lies has a varying deflecting angle.Upon this and through the principle of energy variation,the corresponding Euler's equation,which has the primary integral,can be obtained.After some subsidiary factors were neglected,the analytic solution was achieved.Applying these formulas to a hyperbolic model of diaphragm,the results show that the octahedral shear stress varying less along either radial or thickness direction,but fluctuated greatly and periodically along circumferential direction,thus the unsymmetrical bending affects the material's fatigue significantly.